Chapter 2 - Linear and Quadratic Functions - Section 2.5 Inequalities Involving Quadratic Functions - 2.5 Assess Your Understanding - Page 164: 37

$x=4$

We need to simplify the inequality $(x-4)^2\leq 0$ We know that the square of a real number is non-negative, so the left side of the equation is never negative and we can write: $(x-4)^2=0$. The next step is to evaluate this equation to obtain: $$(x-4)^2=0\\ \sqrt{(x-4)^2}=\pm \sqrt{0}\\ x=4$$ Therefore, the solution to the inequality $(x-4)^2\leq 0$ is: $x=4$